A 5-SPU robot with collinear universal joints is well
suited to handling an axisymmetric tool, since it has 5 controllable
DoFs and the remaining one is a free rotation around the tool. The
kinematics of such a robot having also coplanar spherical joints
has previously been studied as a rigid subassembly of a Stewart-
Gough platform, it being denoted a line-plane component. Here
we investigate how to move the leg attachments in the base and
the platform without altering the robot’s singularity locus. By
introducing the so-called 3D space of leg attachments, we prove
that there are only three general topologies for the singularity
locus corresponding to the families of quartically-, cubicallyand
quadratically-solvable 5-SPU robots. The members of the
last family have only 4 assembly modes, which are obtained
by solving two quadratic equations. Two practical features of
these quadratically-solvable robots are the large manipulability
within each connected component and the fact that, for a fixed
orientation of the tool, the singularity locus reduces to a plane.